Kalam Kinetic Battery
The following is wildly speculative. It is the beginning of a search for a kinetic energy alternative to microwave transmission of space solar power to the ground. It describes a problem that, even confined to the equatorial plane and without the influence of multibody gravity, may have more constraints than degrees of freedom. It could be misused as a weapon. However, if a solution can be found among all the non-solutions, it could revolutionize the space solar power concept.
I presented Server Sky and Launch Loop to the 2010 International Space Development Conference in Chicago. The "video guest of honor" was Dr. A.P.J. Abdul Kalam, the rocket scientist who developed India's first space launch rocket, and was president of India from 2002 to 2007. Not bad, for an apostate Muslim and Tamil technical geek! Dr. Kalam gave a video linkup presentation about space solar power for India, and answered questions afterward (not enough - the foolish AV crew at the conference cut him off for the next session. 
).
I briefly mentioned Server Sky, and asked about providing data service to rural India. Dr. Kalam responded with an idea for providing batteries for children's computers, delivered from space. Or at least that is the way it sounded with my hearing problem. It did not make sense at the time, but it led to this idea, so I will give Dr. Kalam naming credit, unless he or his colleagues ask me not to. If this does not work, it is my problem, not his.
Space solar power is very difficult to do. The power can be collected with large arrays of thinsats, like server sky except optimized for power transmission rather than computation. Energy on the ground can be stored in PowerLoops. But sending power from orbit to the ground is nearly impossible. The best idea people have had so far is sending down beams of microwaves from gigantic antennas to gigantic receivers on the ground. This would be ridiculously expensive, inefficient, interferes with GEO satellite communication, and is damaging to wildlife (and people) caught in the beam. It might be better to use 20THz infrared, but we don't know how to do that efficiently, and atmospheric transmission is poor.
So why not send down "batteries"? Not literally, chemical batteries have low energy density, and getting the discharged ones back up to be charged would require far more energy than they store, even with launch loops launching them up there.
So instead of using chemical batteries brought to the surface, we can instead send down "kinetic batteries", iron bolts much like John Knapman's space cable bolts, at very high speed and containing a heck of a lot of kinetic energy. In honor of Dr. Kalam, I will call these Kalam Kinetic Batteries.
Imagine a vertical bolt accelerator, very long, in an orbit a bit below geosynchronous, but in a 24 hour orbit. How does that happen? A lower than GEO "24 hour orbit" will soon fall towards earth, an ellipse with shorter than 24 hour period. But what if we add centrifugal force by firing a heck of a lot of bolts downwards at very high speed?
The inwards radial velocity and tangential velocity of the bolts can be designed so they miss the earth, almost, grazing above the atmosphere at perhaps 110 kilometer altitude. There, they are precisely (VERY precisely) steered into the mouth of a linear decelerator; they are slowed, energy is taken out, and they exit the decelerator at much lower speed, in an elliptical orbit takes them back to the top of the accelerator. We may be able move kilowatts per kilogram of bolt this way.
Overall, the problem is building a geosynchronous system that must stay continuously aligned to high precision, and cannot stop, even while tidal effects from the moon, the sun, and Jupiter are changing the shape of the gravitational field in which it operates. Our degrees of freedom include the position and velocity of the accelerator and decelerator exits (12 degrees of freedom) relative to the 10 degrees of freedom (position and velocity direction) of the entrances. Super-accurate characterization of the gravity field, and micron per second control over bolt exit velocity, will be required, with some form of mid-course correction, or bolts will collide with the rim of the breeches of the accelerator or decelerator. The accelerator structure is not tied to the earth, and will be too long for lateral stiffness to play a roll; it must be shaped with gravity and tension from tethers and weights hanging above and below geosynchronous orbit.
The system must close the loop on the angular momentum of the bolts throughout their journey; obviously, we can neither add nor subtract large amounts of angular momentum from our accelerator in orbit, or the geometry of the orbits will no longer line up with a fixed position decelerator breech.
Another problem is aiming and orienting the bolts VERY precisely. We have a few tricks - the bolts can contain GPS-like receivers and location transmitters, and control systems can track their position down to the millimeter with server sky tracking arrays. Near the earth, they are passing through the earth's magnetic field, and perhaps we can modify their trajectory (very slightly) by charging or discharging them with a distant electron gun. We and also play tricks with light pressure, by rolling mirrored surfaces into solar (or power laser) light pressure. But these are very small tweaks. We don't want to expend reaction mass, unless we stop bolts at the near-GEO station for refueling.
The decelerator grazes the top of the atmosphere and is in line with the equator. Bolts enter with the velocity vector (if not the speed/magnitude itself) precisely aligned to the breech. The bolt will travel many kilometers before much energy is removed, or the trajectory changes significantly. We can expect wide breeches equipped with lateral actuators and strong magnetic deflectors, narrowing the path of the bolt over the first few hundred kilometers to align it precisely with the decelerator motor.
One accelerator possibility is to build a tethered structure with the bolt launcher above GEO, and a mass hanging below - this will have "extra" angular momentum at launch, which allows the bolt to arrive with excess velocity (and excess angular momentum) near the earth. Wild hand-waving, more invention needed!
Another possibility. We can move bolts around on a curved track on the earth, and fire them back at different angles and lower speeds than they are captured. If we fire the bolts from the station towards earth in a retrograde direction, at very high speed, they provide forward orbital thrust. If they arrive in a manner resembling the CaptureRail, with insufficient angular momentum, they create reverse orbital thrust. If these are balanced, then the total orbital thrust may balance to zero. Perhaps we can even balance them in detail, all along the accelerator/decelerator track, by controlling acceleration and deceleration to match the generation from local solar panels along the track. On the earth, the bolts are returned to the surface and curved in a 180 degree arc to complete the loop.
Total cycle time for a bolt will be on the order of 8 hours. Assuming a arrival maximum speed at the earth (at 100km altitude) of 16 km/s, and a launch return velocity of 10.5 km/s, a kilogram of bolt delivers 73 megajoules of energy every 8 hours, averaging 2530 watts; about 2.5 watts per gram. This compares favorably to the 1 watt per gram of solar energy we can capture with server sky thinsat technology, though we will need quite a large accelerator and power conversion system in orbit. The bolts can be mostly dumb iron, which can be launched from the moon - the lowland rocks are almost 13% iron.
For comparison, the two conductors of the Pacific DC Intertie each weigh about 10 metric tonnes per kilometer (not counting the support towers!) and carry 3100 megawatts for 1360 kilometers from Oregon to Southern California. Total weight of conductor - 27000 tonnes, or about 115 watts per kilogram. 5% of the power density for 4% of the distance!
All this assumes we can adjust the system to deal with lunar and solar tides, of course.